Download or read book Regular Densities of Invariant Measures for Nonlinear Stochastic Equations written by G. Da Prato and published by . This book was released on 1992 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Invariant Measures for Stochastic Partial Differential Equations and Splitting up Method for Stochastic Flows written by Juan Yang and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis consists of two parts. We start with some background theory that will be used throughout the thesis. Then, in the first part, we investigate the existence and uniqueness of the solution of the stochastic partial differential equation with two reflecting walls. Then we establish the existence and uniqueness of invariant measure of this equation under some reasonable conditions. In the second part, we study the splitting-up method for approximating the solu- tions of stochastic Stokes equations using resolvent method.

Download or read book Invariant Measures for Stochastic Partial Differential Equations and Splitting up Method for Stochastic Flows written by Juan Yang and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Existence Uniqueness and Invariant Measures for Stochastic Semilinear Equations on Hilbert Spaces written by A. Michalik and published by . This book was released on 1996-01-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Large Deviations and Invariant Measures for Stochastic Partial Differential Equations in Infinite Dimensions written by Tiange Xu and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Invariant Measures for Semilinear Stochastic Equations written by G. Da Prato and published by . This book was released on 1991 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Approximation of Stochastic Invariant Manifolds written by Mickaël D. Chekroun and published by Springer. This book was released on 2014-12-20 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations. These approximations take the form of Lyapunov-Perron integrals, which are further characterized in Volume II as pullback limits associated with some partially coupled backward-forward systems. This pullback characterization provides a useful interpretation of the corresponding approximating manifolds and leads to a simple framework that unifies some other approximation approaches in the literature. A self-contained survey is also included on the existence and attraction of one-parameter families of stochastic invariant manifolds, from the point of view of the theory of random dynamical systems.

Download or read book Stochastic Delay Equations and Invariant Measure for the Wave Equation with Noise written by Zhao, Xi and published by . This book was released on 2007 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is divided into two major parts. First we study the moment stability of the trivial solution of a linear differential delay equation in the presence of additive and multiplicative white noise. The stability of the first moment for the solutions of a linear differential delay equation under stochastic perturbation is identical to that of the unperturbed system. However, the stability of the second moment is altered by the perturbation. We obtain, using Laplace transform techniques, necessary and sufficient conditions for the second moment to be bounded. Then we establish the stability criteria for stochastic differential equations with Markovian switching using the comparison principle. These criteria include stability in probability, asymptotic stability in probability, stability in the pth mean, asymptotic stability in the pth mean and the pth moment exponential stability of such equations. Next, we study the uniqueness of the invariant measure for the wave equation with noise. We will use a coupling technique and others from the theory of Markov chains on general state spaces. The application of these Markov chain results leads to straightforward proofs of ergodicity of SDEs. The key points which need to be verified are the existence of a Lyapunov function including returns to a compact set, a uniformly reachable point from within that set and some smoothness of the probability densities.

Download or read book Theoretical and Numerical Analysis of Invariant Measures of Viscous Stochastic Scalar Conservation Laws written by Sofiane Martel and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This devoted to the theoretical and numerical analysis of a certain class of stochastic partial differential equations (SPDEs), namely scalar conservation laws with viscosity and with a stochastic forcing which is an additive white noise in time. A particular case of interest is the stochastic Burgers equation, which is motivated by turbulence theory. We focus on the long time behaviour of the solutions of these equations through a study of the invariant measures. The theoretical part of the thesis constitutes the second chapter. In this chapter, we prove the existence and uniqueness of a solution in a strong sense. To this end, estimates on Sobolev norms up to the second order are established. In the second part of Chapter~2, we show that the solution of the SPDE admits a unique invariant measure. In the third chapter, we aim to approximate numerically this invariant measure. For this purpose, we introduce a numerical scheme whose spatial discretisation is of the finite volume type and whose temporal discretisation is a split-step backward Euler method. It is shown that this kind of scheme preserves some fundamental properties of the SPDE such as energy dissipation and L^1-contraction. Those properties ensure the existence and uniqueness of an invariant measure for the numerical scheme. Thanks to a few regularity estimates, we show that this discrete invariant measure converges, as the space and time steps tend to zero, towards the unique invariant measure for the SPDE in the sense of the second order Wasserstein distance. Finally, numerical experiments are performed on the Burgers equation in order to illustrate this convergence as well as some small-scale properties related to turbulence.

Download or read book Stochastic PDE s and Kolmogorov Equations in Infinite Dimensions written by N.V. Krylov and published by Springer. This book was released on 2006-11-15 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kolmogorov equations are second order parabolic equations with a finite or an infinite number of variables. They are deeply connected with stochastic differential equations in finite or infinite dimensional spaces. They arise in many fields as Mathematical Physics, Chemistry and Mathematical Finance. These equations can be studied both by probabilistic and by analytic methods, using such tools as Gaussian measures, Dirichlet Forms, and stochastic calculus. The following courses have been delivered: N.V. Krylov presented Kolmogorov equations coming from finite-dimensional equations, giving existence, uniqueness and regularity results. M. Röckner has presented an approach to Kolmogorov equations in infinite dimensions, based on an LP-analysis of the corresponding diffusion operators with respect to suitably chosen measures. J. Zabczyk started from classical results of L. Gross, on the heat equation in infinite dimension, and discussed some recent results.

Download or read book Invariant Measures for a Class of Stochastic Evolution Equations written by Anna Rusinek and published by . This book was released on 2006 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Dissipativity and Invariant Measures for Stochastic Navier Stokes Equations written by Franco Flandoli and published by . This book was released on 1993 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Harmonic Analysis and Nonlinear Partial Differential Equations written by Tohru Ozawa and published by . This book was released on 2010 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Invariant Measures for a Stochastic Porous Medium Equation written by Giuseppe Da Prato and published by . This book was released on 2003 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Method of Constructing Invariant Measures at Fixed Mass written by Justin Thomas Brereton and published by . This book was released on 2018 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Invariant measures are a useful tool in constructing and analyzing solutions u(t,x) to nonlinear dispersive partial differential equations, especially when a deterministic well-posedness result is not known, and have been studied extensively since the formative work of Bourgain in the 1990s. Due to a wealth of research in recent years, most dispersive PDEs are known to admit an invariant measure with little or no restriction placed on the profile of the initial data u_0 = u(0,x). This prompts one to analyze the ergodicity of such a measure. Unfortunately there has been little progress on decomposition of these measures into invariant measures supported on smaller subsets of the initial data space. Oh and Quastel constructed an invariant measure for each fixed mass and momentum for the NLS equation on T, but there has only been this isolated result. In this thesis we present a more general method of constructing invariant measures supported on H^(1/2-)(T) ∩ {

Download or read book Invariant Measure for the Stochastic Ginzburg Landau Equations written by Marc Barton-Smith and published by . This book was released on 2001 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Invariant Measures for Random Dynamical Systems written by Katarzyna Horbacz and published by . This book was released on 2008 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: